### Citation:

### Abstract:

In this thesis, we use analytic approximate models of cosmologicalgravitational dynamics to study a variety of astrophysical systems. Webegin with the development of a new analytic collapse model in which thecollapsing region is treated as a homogeneous triaxial ellipsoid actedon by cosmological tidal shear. By performing a Monte Carlo sampling ofthe initial conditions, the ellipsoid model can predict thedistributions of angular momenta and axis ratios of collapsing regions.We then apply this and other analytic tools to certain astrophysicalsituations. In considering the origin of the black holes that powerquasars, we consider the likelihood of objects to be formed withsufficiently little angular momentum as to proceed to collapse to ablack hole; using the ellipsoid model, we estimate the number density ofblack holes formed in this manner to be ~ 10^{-3} Mpc ^{-3}. Next, westudy the clustering of Lyalpha clouds around the massive host of thequasar and show that this can produce clouds with redshifts exceedingthat of the quasar and alter the inferred ultraviolet background fromthe analysis of the proximity effect. We then consider the variation inthe relation between halo masses and velocity dispersions caused byvariations in their merger histories and show that the resulting scatteris larger than that observed for the Tully-Fisher relation. This arguesthat the Tully-Fisher relation does not result simply from theuniversality of halo properties but rather from feedback processesduring galaxy formation. Finally, we apply an exact solution for thesteady-state, self-gravitating, isothermal cylinder to construct amethod for estimating the mass per unit length of linear structures inredshift surveys. Tests of the method against N-body simulations suggest